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**Applied functional analysis.**
*(English)*
Zbl 0461.46001

Ellis Horwood Series in Mathematics and its Applications. Chichester: Ellis Horwood Limited, Publishers. New York etc.: Halsted Press: a division of John Wiley & Sons. 386 p. £25.00 (1981).

### MSC:

46-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis |

46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |

46F05 | Topological linear spaces of test functions, distributions and ultradistributions |

46B03 | Isomorphic theory (including renorming) of Banach spaces |

46B10 | Duality and reflexivity in normed linear and Banach spaces |

46E15 | Banach spaces of continuous, differentiable or analytic functions |

46E20 | Hilbert spaces of continuous, differentiable or analytic functions |

46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |

46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |

46F10 | Operations with distributions and generalized functions |

46F12 | Integral transforms in distribution spaces |

47A05 | General (adjoints, conjugates, products, inverses, domains, ranges, etc.) |

47A10 | Spectrum, resolvent |

47A53 | (Semi-) Fredholm operators; index theories |

47A70 | (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces |

47B06 | Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators |

47B38 | Linear operators on function spaces (general) |

47D03 | Groups and semigroups of linear operators |

47E05 | General theory of ordinary differential operators |

47F05 | General theory of partial differential operators |

47Gxx | Integral, integro-differential, and pseudodifferential operators |

47H10 | Fixed-point theorems |

47J05 | Equations involving nonlinear operators (general) |

47J25 | Iterative procedures involving nonlinear operators |

49R50 | Variational methods for eigenvalues of operators (MSC2000) |

34A30 | Linear ordinary differential equations and systems |

34A35 | Ordinary differential equations of infinite order |

34L99 | Ordinary differential operators |

34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |

34D99 | Stability theory for ordinary differential equations |

34E99 | Asymptotic theory for ordinary differential equations |

35A05 | General existence and uniqueness theorems (PDE) (MSC2000) |

35A08 | Fundamental solutions to PDEs |

35A15 | Variational methods applied to PDEs |

35A22 | Transform methods (e.g., integral transforms) applied to PDEs |

35B32 | Bifurcations in context of PDEs |

35B35 | Stability in context of PDEs |

35C20 | Asymptotic expansions of solutions to PDEs |

35E05 | Fundamental solutions to PDEs and systems of PDEs with constant coefficients |

35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |

35K05 | Heat equation |

35L05 | Wave equation |

35J15 | Second-order elliptic equations |

35J20 | Variational methods for second-order elliptic equations |

35J30 | Higher-order elliptic equations |

35J35 | Variational methods for higher-order elliptic equations |

35P05 | General topics in linear spectral theory for PDEs |

42A16 | Fourier coefficients, Fourier series of functions with special properties, special Fourier series |

42A20 | Convergence and absolute convergence of Fourier and trigonometric series |

42A65 | Completeness of sets of functions in one variable harmonic analysis |

42B05 | Fourier series and coefficients in several variables |

45B05 | Fredholm integral equations |

45C05 | Eigenvalue problems for integral equations |

45D05 | Volterra integral equations |

45G10 | Other nonlinear integral equations |

70J25 | Stability for problems in linear vibration theory |

70K20 | Stability for nonlinear problems in mechanics |

70K30 | Nonlinear resonances for nonlinear problems in mechanics |

37G99 | Local and nonlocal bifurcation theory for dynamical systems |

76R99 | Diffusion and convection |

76U05 | General theory of rotating fluids |